One Spin, Speeds That Scale With r

You'll learnthat points on one disk share angular velocity but linear speed scales with radius.

Every point on a rigid disk shares a single angular velocity, yet no two points at different radii move at the same speed. The radius is the exchange rate between the spin they share and the linear motion they don’t — and it prices arc length, speed, and both pieces of acceleration.

8 STEPS · 6 QUICK CHECKS · v2

ROTATION LAB

Before you start

What you're looking at

One rigid disk turning at ω = 4 rad/s, with an inner rider at r = 0.5 m and an outer rider at r = 1.0 m on the same spoke.

The question

The two riders share one motion, so which one moves faster?

Watch for

The blue speed arrows. Both riders share ω, but the outer arrow grows twice as long.

What the symbols mean

Shared ω = 4 rad/s; r = distance from axis; blue = tangential velocity v = rω (m/s).

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